$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-2;}{\phantom{;}5x^{3}+7x^{2}+14x\phantom{;}+32\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-2\overline{\smash{)}\phantom{;}5x^{4}-3x^{3}\phantom{-;x^n}+4x\phantom{;}+8\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-2;}\underline{-5x^{4}+10x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-5x^{4}+10x^{3};}\phantom{;}7x^{3}\phantom{-;x^n}+4x\phantom{;}+8\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n;}\underline{-7x^{3}+14x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-7x^{3}+14x^{2}-;x^n;}\phantom{;}14x^{2}+4x\phantom{;}+8\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n;}\underline{-14x^{2}+28x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-14x^{2}+28x\phantom{;}-;x^n-;x^n;}\phantom{;}32x\phantom{;}+8\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n-;x^n;}\underline{-32x\phantom{;}+64\phantom{;}\phantom{;}}\\\phantom{;;;-32x\phantom{;}+64\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}72\phantom{;}\phantom{;}\\\end{array}$

$5x^{3}+7x^{2}+14x+32+\frac{72}{x-2}$